Up to 10,000 homes a day could get a visit from 'Covid marshals' to ensure they are quarantining after foreign travel.
The amber list covers many popular locations for Brits including Spain, France, Italy and Greece.
People returning from amber countries must take two post-arrival tests.
However, ministers have stressed that now is not the time to be visiting such locations.
Transport Secretary Grant Shapps said: “you should not be travelling to these places right now”.
On Sunday, Health Secretary Matt Hancock told Times Radio people should not travel to places on the amber or red lists “unless it’s absolutely necessary, and certainly not for holiday purposes”.
The PM has also stressed countries on the amber list were “not somewhere where you should be going on holiday”.
They are also required to self-isolate at home for 10 days, although they can reduce that time if they take an additional negative test on day five.
If those returning are not home when the visit takes place, they could be reported to the police.
Increase in self-isolation checks
The Government is currently carrying out around 1,000 checks a day, but this will be stepped up as more people head away now the travel ban has eased.
Those returning to the UK from countries on the Government’s “amber list” are required to self-isolate for a period of 10 days at home and get a PCR test on days two and eight.
It was reported last week that the Home Office had hired a private security firm to carry out these visits, with staff from Mitie making sure people are self-isolating where required.
The Government hopes its contract with Mitie will increase compliance among arrivals from countries on the “amber list”.
NHS Test and Trace currently rings passengers who have just arrived in the UK to check they are observing the rules, but if they suspect wrongdoing then call handlers can pass the case onto local police forces who will then make a home visit.
Those who fail to comply with their legal duty to self-isolate at home on their return to the UK can be fined £1,000, which increases up to £10,000 for repeat offences.
Travellers returning from countries on the “green list” do not have to self-isolate, but are required to take a PCR test on day two after their arrival.
Individuals arriving from “red list” countries will need a negative pre-departure Covid test, as well as undergoing a managed quarantine at a hotel for 10 days and a PCR test on days two and eight.
‘You should not be going to an amber list country on holiday’
The increased checks on those required to self-isolate comes as Prime Minister Boris Johnson and Health Secretary Matt Hancock recently sought to clear up confusion over whether or not people are able to travel to countries on the “amber list”.
Earlier this week Environment Secretary George Eustice said people could go to amber-listed countries to visit family or friends as long as they observed quarantine rules on their return.
Welsh Secretary Simon Hart also said “some people might think a holiday is essential” and therefore a valid reason to travel.
However, the Prime Minister then insisted the position was “very clear” and that people should only travel to an amber list country “for some extreme circumstance, such as the serious illness of a family member”.
Mr Johnson told MPs: “You should not be going to an amber list country on holiday.”
Health Secretary Mr Hancock also told a Downing Street press conference on Wednesday (19 May): “We have been absolutely crystal clear that you should not go to an amber or red list country on holiday, you should only go in exceptional circumstances.”
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